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Table of Content

    10 December 2021 Volume 40 Issue 12
      
    Using charge qubits to facilitate the teaching of matrix mechanics
    TU Tao, LI Chuan-feng, GUO Guang-can
    College Physics. 2021, 40(12):  1.  doi:10.16854 / j.cnki.1000-0712.210108
    Abstract ( 400 )   PDF (386KB) ( 603 )  
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    The representation and calculation of matrix mechanics is a very important element

    in the quantum mechanics course. The two-level system serves as a simple example to deepen

    students' understanding of matrix me- chanics. However,the current textbooks give rather limited

    attention to the two-level system. In this paper,we intro- duce a system in the research frontier

    of quantum information: the charge qubit. In the teaching,the system is first modeled using a

    Hamiltonian operator to describe the occupation and tunneling processes of a single electron in two

    quantum dots. Then,the state and the time evolution of the system are obtained by three methods

    such as energy ei- genfunctions representation,solving the time-dependent Schrödinger equation and

    solving the equation of motion for the expectation value of an operator. Finally,by comparing the

    theoretical analysis and experimental results,students can find that the theory is consistent with

    the experiment. Thus these teaching contents can help students to grasp more intuitively

    and deeply the quantum mechanical laws and calculations with the matrix mechanics representation.

    Ab initio atomistic thermodynamics method and analysis of reaction phase diagrams
    CHU Xing-li, ZHANG Yan-xing, DU Ai-hui
    College Physics. 2021, 40(12):  8.  doi:10.16854 / j.cnki.1000-0712.210185
    Abstract ( 286 )   PDF (351KB) ( 104 )  
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    Equilibrium conditions and equilibrium properties of multiphase systems are

    important contents in thermodynamics teaching. In order to make students understand the

    basic theory and the knowledge of thermody- namics deeply,the ab initio atomistic

    thermodynamics method based on principle of phase equilibrium is analyzed in detail,and the

    corresponding academic research results are introduced into teaching,which not only help to improve

    students'understanding and application of thermodynamic equilibrium properties,but also provide a

    certain reference for design of teaching contents.

    Calculation of volume at both ends of liquid bridge between two parallel plates
    YANG Li, CHEN Zhen-yu, XIAO Hua-peng
    College Physics. 2021, 40(12):  12.  doi:10.16854 / j.cnki.1000-0712.210220
    Abstract ( 220 )   PDF (294KB) ( 72 )  
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    When a small amount of liquid is adsorbed on two solid surfaces with tiny spacing,the

    phenomenon of liquid bridge occurs. In this paper,the liquid bridge between two narrow and long

    flat plates is taken as the re- search object,and the three-dimensional liquid bridge model is established to calculate the saddle-shaped liquid volume at both ends of the liquid bridge.The relationship between the characteristic parameters of the liquid bridge shape and the volume is obtained.

    The influence of coaxial iron tube and its defects on axial magnetic field in excitation solenoid
    MA Feng-xiang, CHU Wei, WANG Xin-yue
    College Physics. 2021, 40(12):  15.  doi:10.16854 / j.cnki.1000-0712.210298
    Abstract ( 219 )   PDF (204KB) ( 67 )  
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    On the basis of Hall effect measurement of magnetic field in excitation

    solenoid,the experimentalcontent of magnetic field measurement was expanded in this article by placing an iron tube

    coaxially in solenoid. Ex-perimental result showed that the intact iron tube in excitation solenoid hac almost

    zero internal magnetic field. However,if the iron tube had material defects,an obvious magnetic

    leakage signal could be measured at the corre- sponding axis position. This extended experiment

    not only strengthens the experimental training of magnetic field measurement,but also enriches the basic experimental techniques of magnetic shielding and defect magnetic flux leakage detection.

    Acousto-optic diffraction of plane light wave with spherical acoustic wave
    XI Feng, HU Li
    College Physics. 2021, 40(12):  20.  doi:10.16854 / j.cnki.1000-0712.200544
    Abstract ( 213 )   PDF (266KB) ( 110 )  
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    The acousto - optic interaction of plane light wave with spherical acoustic in

    spherical cavity with open ends is investigated theoretically and experimentally. On basis

    of the diffraction theory of light,the intensity distribution of diffracted light is

    deduced. And then,an image of the diffracted light is displayed by numerical calcu- lation. On the

    other aspect,the acousto-optic diffraction is measured with our apparatus. The measured wavelength

    of acoustic wave is coincided with that of excited spherical acoustic wave.

    Numerical simulation of aperture diffraction with arbitrary brightness
    FANG Hui-wen, YANG Jin-hong, HE Sheng-nan, WEI Yu-jiao, ZHANG Wu-ji, WANG Wei-hua
    College Physics. 2021, 40(12):  24.  doi:10.16854 / j.cnki.1000-0712.210128
    Abstract ( 241 )   PDF (468KB) ( 90 )  
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    Based on Matlab software platform,the Huygens Fresnel formula is processed by

    programming. The brightness values of various aperture light sources are realized by using

    picture pixels,and the complex amplitude distribution on the light screen is calculated by

    Matlab cycle. The numerical simulation of near-field / far-field dif- fraction pattern of

    arbitrary shape and brightness aperture can be realized simply and quickly,and the

    diffraction pattern of arbitrary shape and brightness aperture are given. In the process of

    near-field diffraction to far-field dif- fraction,the change of central light intensity

    gradually decreases ( from Fresnel diffraction to Fraunhofer diffrac- tion) ; in the

    process of simulating the diffraction characteristics of regular polygon hole,it is verified that

    when the number of regular polygon edges tends to infinity,the diffraction image is

    circular hole diffraction; finally,a nu- merical example is given for diffraction pattern of

    arbitrary shape and brightness hole.

    The experimental test of Born's rule
    JIN Fang-zhou, PENG Yu-ping, LI Qing-rong, ZHU Xiao-fei
    College Physics. 2021, 40(12):  29.  doi:10.16854 / j.cnki.1000-0712.210030
    Abstract ( 222 )   PDF (323KB) ( 72 )  
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    Born's rule is one of the basic assumptions of quantum mechanics. It establishes a direct correspon- dence between the mathematical form of quantum mechanics and experimental measurement. However,some gener-alized quantum theories have proposed amendments to Born's rule, allowing the existence of multi - order interference terms. Recently,many researchers have tested Born's rule on different experimental systems,and the results obtained are consistent with Born's rule predictions within the error. This article introduces the methods of Born rule in optical and spin systems,and then proposes an improved method in spin system from the perspective of changing the observable. We hope that it is helpful for the understanding and research of Born rules in the future.
    Theoretical analysis for the influence of particles inside the flue to beam quality
    LIU Jian-ping, FU Ji-zheng, LIN Yong
    College Physics. 2021, 40(12):  33.  doi:10.16854 / j.cnki.1000-0712.210165
    Abstract ( 191 )   PDF (162KB) ( 37 )  
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    Optical method for measurement of particulate concentration in flue basing on optical scintillation is an important non-intrusive technology. In order to research the influence of particles to optical intensity,the inten- sity degradation of probing beam is simulated basing on Lambert-Beer's law,when particle size distribution satisfies logarithm normal distribution and Gauss distribution,respectively. In the calculation,the relationship between ex- tinction coefficient and species and the middle level diameters are pre-calculated. The results show that,when the particle size distribution satisfies logarithm normal distribution,the intensity degradation of probing beam is more significantly. The optical intensity exhibites the same changes when the particle size decreases gradually.
    Discussion of uniqueness of fixed-point motion rotation axis and vectoriality of Euler angular displacement
    XU Chen-hao, ZHANG Ya-hong
    College Physics. 2021, 40(12):  36.  doi:10.16854 / j.cnki.1000-0712.210223
    Abstract ( 228 )   PDF (258KB) ( 100 )  
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    The purpose of this paper is to rigorously prove the uniqueness of the equivalent and instantaneous rotation axes of the fixed-point motion of a rigid body by the analytical method,and to investigate the conditions under which the Euler angular displacement vectoriality of the fixed-point motion holds. The uniqueness of the e- quivalent axis is proved by using the properties of the transition matrix and its eigenvector,and on this basis,it is proved that the finite Euler angular displacement is not a vector. Then the uniqueness of the instantaneous axis is proved,and based on the differential operation of the transition matrix,it is concluded that the infinitesimal Euler angular displacement is a vector,and the analytic relationship between the direction vector of the instantaneous axis and the Euler angle is given. The rigorous proof and analysis of the conclusions related to the fixed-point motion based on matrix operations enrich and improve the description of the fixed-point motion of a rigid body,and the proof and analysis process further demonstrate the advantages of matrices and their eigenvalue properties in the anal- ysis of complex rigid body motion.
    The landing problem of a thin cylinder
    WU Jia-yi
    College Physics. 2021, 40(12):  41.  doi:10.16854 / j.cnki.1000-0712.210056
    Abstract ( 150 )   PDF (425KB) ( 105 )  
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    The landing problem of a thin cylinder is abstracted from the spinning-landing process of a washba- sin or a round plate in everyday life. This problem is analytically difficult but has a fascinating physical picture. In this paper,different approximate methods are used to gradually characterize the actual situation. The motion is shown using numerical simulation. The initial motion of a thin cylinder before it falls onto the ground can be approx-imated as a fixed point rotation and in good agreement with the reality,however,the whole motion is not fix point rotation completely. So the general motion of this rigid is studied which leads to interesting results. The initial angu- lar velocity of precession and nutation sculptured the state of motion,while force of friction plays a vital role in cau- sing energy loss of the system.
    A brief derivation of Maxwell's speed distribution function by the character of three-dimensional sphere
    SUN Yu-chen, ZHANG Zhao-long
    College Physics. 2021, 40(12):  47.  doi:10.16854 / j.cnki.1000-0712. 210072
    Abstract ( 257 )   PDF (128KB) ( 127 )  
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    In this paper,Maxwell's speed distribution function is derivated by using the character of three-di- mensional sphere and the relation between the Maxwell's velocity distribution and the Maxwell's speed distribution without solving any partial differential equations.
    A new relation between angular momentum and non-commutativity of different components of momentum for a charge in a magnetic field
    CHEN Jun-feng, XIE Wei-xin, WANG Xin, LIU Quan-hui
    College Physics. 2021, 40(12):  49.  doi:10.16854 / j.cnki.1000-0712.210252
    Abstract ( 279 )   PDF (146KB) ( 92 )  
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    It is known that for a charge particle in a magnetic field,the Poisson bracket or commutator of dif- ferent components of the momentum is proportional to a component of the magnetic field.It is demonstrated that it is proportional a component of the mechanical angular momentum. This new relation can be considered as a manifesta- tion of Maxwell's qualitative statement that magnetism is essentially rotational in nature.
    Research on the damped motion of a small magnet falling in a metal tube
    WANG Kai-ze, TAO Xiao-ping
    College Physics. 2021, 40(12):  52.  doi:10.16854 / j.cnki.1000-0712.210140
    Abstract ( 251 )   PDF (189KB) ( 182 )  
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    The paper quantitatively studies the motion of the small magnet falling on the metal

    tube,gives the relevant theoretical formulas,and designs experiments that measure physical

    parameters such as the falling speed of the small magnet,the magnetic moment of the small magnet

    and the resistivity of the metal tube.

    Simple measurement of the axis distance and interpupillary distance
    ZHOU Si-ying¹, CHANG Kai-ge², MAO Sheng-chun², GAO Bo²
    College Physics. 2021, 40(12):  55.  doi:10.16854 / j.cnki.1000-0712.210044
    Abstract ( 415 )   PDF (708KB) ( 67 )  
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    If the interpupillary distance does not match the axis distance of one's glasses,the

    scene would be deformed,distorted and blurred,and this could result in visual fatigue and

    irreversible damage to the eyes. In this paper a measurement scheme by using laser pen,ruler and

    mobile phone is proposed. By analyzing the principle of optical imaging,the measurement models of

    axis distance in four position cases of laser pen are established,and the calculation formulas of

    two glasses with the same or the different degrees are given. Then a platform is built to do ex-

    periment,and the factors affecting on the accuracy are analyzed. Tracker video analysis software is

    also used to fur- ther reduce the measuring error. Finally,through taking pictures by using mobile

    phone,the interpupillary distance is accurately measured. Thus conveniently measuring the

    interpupillary distance and the axis distance and accurately judging whether they match or not are

    realized.

    A rough measurement of s- and p-quantum defects of Sodium based on general physical experiments
    DING You-ye, ZHANG San-jun, YIN Ya-ling
    College Physics. 2021, 40(12):  62.  doi:10.16854 / j.cnki.1000-0712.210080
    Abstract ( 305 )   PDF (241KB) ( 63 )  
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    The adjustment of spectrometer and measurement of the prism's refrective index is a classic,general

    physical experiment. In this experiment,students can directly see the Mercury spectrum

    through prisms,which is vivid,while they do not explore the formation mechanism of atom spectrual lines. On the

    contrary,the experiment of Sodium spectrum is a classic,modern physical experiment. Students

    understand the nature of atoms and spectrual lines through the calculation of quantumn defects and

    the drawing of energy level figures. This experiment combines the thoughts of these two experiments,where students first observe spectrual lines with familiar spectrometers,and calculate the s-and p-quantum defects of Sodium with interpolation methods to understand the characteristics of at- oms. The results ( 1.348 and 0.882,respectively) are in line with the ones carefully calculated,proving that this i- dea is rather practical.

    Optimized algorithm for arbitrary point levitation in ultrasonic phased arrays
     HUANG Jun-kang¹, DENG Kai-xiao¹, FAN Qian-qian¹, LIN Jia-hong¹, HE Qing-lin¹, PENG Li¹, ²
    College Physics. 2021, 40(12):  67.  doi:10.16854 / j.cnki.1000-0712.210107
    Abstract ( 195 )   PDF (1036KB) ( 42 )  
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    The optimization degree of the phase delays of the transducers directly affects the

    precision degree of particle manipulation by the ultrasonic phased arrays. In this paper,an

    improved adaptive genetic algorithm is proposed to optimize the phase delay of each transducer

    in ultrasonic phased arrays. The algorithm not only has the characteristics of fast

    convergence,stable convergence and good optimization effect,but also is insensitive to array size.

    Four levitation points in the space are taken as examples to verify that the algorithm

    has a good optimization effect on arbitrary levitation points in the space. The reliability of the algorithm is verified by

    building acoustic levi- tation experiment of ultrasonic phased arrays to conduct levitation

    experiments.

    Investigation of stability conditions for falling tower
    XIAO Xiang-jun¹, CHEN Ke-jian², LIU Tian-qi¹
    College Physics. 2021, 40(12):  74.  doi:10.16854 / j.cnki.1000-0712.210076
    Abstract ( 388 )   PDF (705KB) ( 177 )  
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    Identical discs are stacked one on top of another to form a freestanding tower. The

    bottom disc can be removed by applying a sudden horizontal force such that the rest of the

    tower will drop down onto the surface and the tower remains standing. Investigate the phenomenon

    and determine the conditions that allow the tower to remain standing. Theoretically,the dynamic

    analysis is carried out by stages,and it is found that the key to judge whether the tower collapses

    lies in the position of the tower at the moment when it hits the ground. In the experiment,the ro-

    tating shaft of the motor is used to drive the rope to pull the disc to exert horizontal

    force,which improves the con- trollability and repeatability of the experiment. The effects of the

    height of the horizontal force point,the ratio of the disc thickness to the radius and the number

    of layers on the stability of the tower are investigated. The theoretical and

    experimental trends are in good agreement,and the differences between them are analyzed and

    explained.